Large deviations of extremes in branching random walk with regularly varying displacements

2018/02/16 by Bhattacharya, Ayan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1802.05938

Abstract

In this article, we consider a branching random walk on the real-line where displacements coming from the same parent have jointly regularly varying tails. The genealogical structure is assumed to be a supercritical Galton-Watson tree, satisfying Kesten-Stigum condition. We study the large deviations of the extremal process, formed by the appropriately normalized positions in the n-th generation and show that the large extreme-positions form clusters in the limit. As a consequence of this, we also study the large deviations of the maximum among positions at the n-th generation.

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